Theta oscillations represent collective dynamics of multineuronal membrane potentials of murine hippocampal pyramidal cells

Theta (θ) oscillations are one of the characteristic local field potentials (LFPs) in the hippocampus that emerge during spatial navigation, exploratory sniffing, and rapid eye movement sleep. LFPs are thought to summarize multineuronal events, including synaptic currents and action potentials. However, no in vivo study to date has directly interrelated θ oscillations with the membrane potentials (Vm) of multiple neurons, and it remains unclear whether LFPs can be predicted from multineuronal Vms. Here, we simultaneously patch-clamp up to three CA1 pyramidal neurons in awake or anesthetized mice and find that the temporal evolution of the power and frequency of θ oscillations in Vms (θVms) are weakly but significantly correlate with LFP θ oscillations (θLFP) such that a deep neural network could predict the θLFP waveforms based on the θVm traces of three neurons. Therefore, individual neurons are loosely interdependent to ensure freedom of activity, but they partially share information to collectively produce θLFP.


Supplementary Figure 3: Optimization of the threshold for θLFP detection.
(a) Cumulative probabilities of the Dice similarity coefficients between pairs of θLFPs among four simultaneously recorded CA1 LFPs (see Fig. 1a) at various SDs (1, 2, 3, and 4) for the threshold of oscillation powers above which θ oscillations were identified. The blue lines indicate real data, whereas the black lines and gray shadow areas indicate the mean values and the 95% confidence intervals, respectively, of 10,000 surrogate data in which all detected θ periods were randomly shuffled along the recording time within each recording site.
(b) The D values of a two-sample Kolmogorov-Smirnov test were calculated from the cumulative distributions in a and plotted against the SDs for the θ thresholds. The D values reached a maximum at a threshold of 2 SDs, which was adopted for the detection of θ oscillations in this study. (a) Correlation coefficients between θLFP and θVm power changes were plotted against the recording time for each dataset. No significant relationship was found between the correlation coefficients and recording times. R = 0.11, P = 0.19, t-test for correlation coefficients, n = 160 cells.
(b) No significant relationship was found between the correlation coefficients and the maximal power of θVm during the entire recording period. R = -0.042, P = 0.60, n = 160 cells.
(c) No significant relationship was found between the correlation coefficients and the mean firing rate of each cell. R = -0.081, P = 0.31, n = 160 cells.
(d) No significant relationship was found between the correlation coefficients and the mean Vm of each cell. R = -0.14, P = 0.076, n = 160 cells. (d, e) Same as b, c, but for a dataset in which a significant positive correlation was observed (R = 0.56, P < 10 -323 , n = 2,479 1-s segments).
(f) Cumulative probability distribution of the correlation coefficients between the θVm powers of all 125 cell pairs. Each red dot indicates a cell pair with a significant correlation.
(g) The correlation coefficients of the θVm powers (calculated in d) plotted against the spatial distance between two somata. The black line indicates the line of best fit based on least-squares regression. R = -0.24, P = 0.033, n = 78 cell pairs.
(h) Relationships of the θVm frequencies between two cells for periods during which they simultaneously exhibited θVms. Each dot indicates a single co-θ period. R = 0.25, P < 10 -changes in the data shown in Fig. 3 and Supplementary Fig. 7. (a) Cumulative probability distribution of the correlation coefficients between the θVm powers of 98 cell pairs, which were included in the analyses for Fig. 3. Each red dot indicates a cell pair with a significant correlation.
(b) Ratios of cell pairs with significantly correlated θVm power changes for the data used in the analyses for Supplementary Fig. 7 (left) and only the data used for the analyses in (e) Four sets of parameters and the validation RMSE for each set. Set 1 was selected because these parameters obtained the smallest validation loss.

θVms between real data and shuffled data.
The same data as in Fig. 5d  (d-f) Same as a-c, but for the low gamma frequency band (25-55 Hz).
(g-i) Same as a-c, but for the slow oscillations (0.5-1 Hz).
(j) LFP power spectrum averaged across all 8 datasets used in the DNN analysis. The most dominant peak was observed between 3 and 10 Hz.
(k) Same as d, but for Vm. Dominant peaks were observed between 3 and 10 Hz.

Vms.
(a) Cumulative probability distributions of the correlation coefficients between θLFP traces and the mean θVm traces of 1, 2, or 3 cells simultaneously recorded. Darker colors indicate the results for a larger number of cells. The correlation coefficients decreased as the number of cells increased, indicating that the mean θVm traces of more cells were less similar to the θLFP trace. D1 vs. 2 cells = 0.029, P1 vs. 2 cells = 6.5×10 -42 , D1 vs. 3 cells = 0.049, P1 vs.